For any affine semigroup S, the set S boolean OR {infinity} has a natural semigroup structure; additionally, if S is endowed with the discrete topology, then the semigroup S boolean OR{infinity} can be studied as the one-point compactification of S. In this article, we study the derivations on semigroup algebra C[S boolean OR{infinity}] in relation to the derivations on semigroup algebra C[S] considering the metrizable topology on C[S boolean OR{infinity}] induced by the one-point compactification topology of S boolean OR{infinity}.